1. Prince in one basket and stone in the other. Prince down. Stone up. Prince stays on the ground. Leave the stone at the top.
2. King in one basket and Queen plus stone in the other. King down. Queen and stone up. King stays on the ground. Queen and stone at the top.
3. Queen in one basket and prince in the other. Queen down. Prince up. Queen stays on the ground. Prince at the top.
4. Prince in one basket and stone in the other. Prince down. Stone up. Prince stays on the ground.

Not going to work. King, Queen and stone are all at the top. First you'd have to pull a basket up, which, even if allowed, will result in two baskets up top. Then King, Queen and stone will all drop. I'd guess they'd break the rope.

Prince goes down alone. Then Queen and stone in one basket, and king in other, King will reach down. Remove stone, and Prince climbs in. in one, Queen in other. Queen will reach down, Prince will go up. Now stone in one basket, Prince in other, Prince will reach down. :)

I think you have to assume that initially the one bucket is empty and sitting at the top of the pulley, and the other is on the ground with the stone in it. When the prince goes down, you just can't say that you then put the queen and stone in one bucket and the king in the other, because one bucket is always on the ground.

Since one of the baskets got 30 kg stone, it is at the ground. Following sequence will bring all 3 down:

1. Prince (36 kg) gets into basket, it will come down to ground and basket with 30 kg stone will reach top.
2. King unloads stone and queen gets in, basket with prince (36 kg) will come to top and queen (42 kg) on ground. Queen stays on ground.
3. King (72 Kg) gets into one basket, prince and stone (36kg + 30kg) in the other. King reaches safely. Now both king and queen are on ground.
4. Prince changes basket. He comes down as other basket got 30 kg rock.

Assume that basket with stone is at bottom (basket2), and empty one is at top (basket1)
1. Queen in basket1, goes down. Basket2 will goto top. Queen land in the ground, so basket2 will come down. Now queen will get into basket 2 (30kg + 42kg).
2. King (78 kg) will get into basket1 and comes down. King will land in the ground. Basket2 will come down, so queen can also land in the ground.
3. Prince get into the basket1 and comes down.

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